Batch reactor

A first-order reaction $A\to B$ whose rate constant depends on temperature through Arrhenius, which we know, and on pH through a curve with no first-principles form, which we do not. The classical fit gives you one set of Arrhenius constants per pH and no way to predict between them. The hybrid model keeps the Arrhenius trunk and adds a small bounded residual network, so one model covers every pH at once and interpolates. Fitted in two stages: CMA-ES for the parametric trunk, then gradients for the residual.

Run it yourself with:

uv run python examples/batch_reactor/train_hybrid.py

Results

Default settings, seed 0: 60 CMA-ES generations for the parametric trunk, then 800 AdamW steps for the residual. The k-reveal plot is the whole story — the parametric trunk cannot see pH, so all its curves are flat, and the hybrid model's curves track the truth across the pH range:

The validation points (triangles) at (20 °C, 5.3) and (30 °C, 6.8) were never fitted. The residual bought one model with the pH shape to approach them, instead of one Arrhenius fit per bin.

The batch-reactor page continues in part two, the RL example, which freezes this fitted trunk and learns a catalyst-activity policy on top of it.